Calculation of solvation free energies of charged solutes using mixed cluster/continuum models

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H+ and 2.0 kcal/mol for Cu2+. Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for HI and >30 kcal/mol for Cu2+. The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancelation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H+ (6 waters) and 27 kcal/mol for Cu2+ (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu2+ (18 waters) and 1 kcal/mol for H+ (10 waters).